A model-based decentralized control design for general interconnected systems

This paper deals with the decentralized control of an interconnected system, where each subsystem has models of all other subsystems (subject to uncertainty). A decentralized controller is constructed based on a reference centralized controller. It is shown that when a priori knowledge of each subsystem about the other subsystems’ models is exact, then the decentralized closed-loop system can perform exactly the same as its centralized counterpart. An easy-to-check necessary and sufficient condition for the internal stability of the decentralized closed-loop system is obtained. Moreover, the stability of the closed-loop system in presence of the perturbation in the parameters of the system is investigated, and it is shown that the decentralized control system is likely more robust than its centralized counterpart. A proper cost function is then defined to evaluate the closeness of the decentralized closed-loop system to the corresponding centralized control system. This enables the designer to obtain the maximum allowable standard deviation for the modelling errors of the subsystems to achieve a relative performance deviation with a sufficiently high probability. Finally, the proposed method is exploited to design a near-optimal decentralized control law with respect to a quadratic cost function, whose performance can, under certain conditions, be equal to the minimum achievable performance index corresponding to the centralized LQR control law. The effectiveness of the proposed method is demonstrated in two numerical examples.